<p>We propose a novel method for detecting a single change-point in count time series, allowing for a structural shift in both the marginal distribution and temporal dependence. The approach employs a copula-based Markov model, with the generalized Poisson distribution governing the marginal distribution to accommodate over-dispersion commonly observed in count data. Dependence between adjacent observations is modeled using parametric copulas, with parameters allowed to differ before and after the change-point. For illustration, we consider two copulas, Clayton and Joe, which are commonly used to capture lower and upper tail dependence, respectively. The change-point is incorporated as an additional model parameter. Estimation of all parameters, including the change-point, is estimated by maximizing the profile likelihood. This optimization is implemented using the Newton–Raphson algorithm. Simulation studies demonstrate that the proposed method provides accurate parameter estimates and reliable change-point detection across a range of scenarios. The practical utility of the model is illustrated through its application to the British coal mining accident data. To promote transparency and reproducibility, the implementation code is provided as online Supplementary Materials.</p>